33,868 research outputs found
Genuine Non-Self-Averaging and Ultra-Slow Convergence in Gelation
In irreversible aggregation processes droplets or polymers of microscopic
size successively coalesce until a large cluster of macroscopic scale forms.
This gelation transition is widely believed to be self-averaging, meaning that
the order parameter (the relative size of the largest connected cluster)
attains well-defined values upon ensemble averaging with no sample-to-sample
fluctuations in the thermodynamic limit. Here, we report on anomalous gelation
transition types. Depending on the growth rate of the largest clusters, the
gelation transition can show very diverse patterns as a function of the control
parameter, which includes multiple stochastic discontinuous transitions,
genuine non-self-averaging and ultra-slow convergence of the transition point.
Our framework may be helpful in understanding and controlling gelation.Comment: 8 pages, 10 figure
Color Reflection Invariance and Monopole Condensation in QCD
We review the quantum instability of the Savvidy-Nielsen-Olesen (SNO) vacuum
of the one-loop effective action of SU(2) QCD, and point out a critical defect
in the calculation of the functional determinant of the gluon loop in the SNO
effective action. We prove that the gauge invariance, in particular the color
reflection invariance, exclude the unstable tachyonic modes from the gluon loop
integral. This guarantees the stability of the magnetic condensation in QCD.Comment: 28 pages, 3 figures, JHEP styl
Comment on Decay
We calculate the rate for decay using Chiral
Perturbation Theory. This isospin violating process results from -
mixing, and its amplitude is proportional to . Experimental information on the branching
ratio for can provide insight into the pattern of
violation in radiative decays.Comment: 7 pages with 2 figures not included but available upon request,
CALT-68-191
Discontinuous percolation transitions in real physical systems
We study discontinuous percolation transitions (PT) in the diffusion-limited
cluster aggregation model of the sol-gel transition as an example of real
physical systems, in which the number of aggregation events is regarded as the
number of bonds occupied in the system. When particles are Brownian, in which
cluster velocity depends on cluster size as with
, a larger cluster has less probability to collide with other
clusters because of its smaller mobility. Thus, the cluster is effectively more
suppressed in growth of its size. Then the giant cluster size increases
drastically by merging those suppressed clusters near the percolation
threshold, exhibiting a discontinuous PT. We also study the tricritical
behavior by controlling the parameter , and the tricritical point is
determined by introducing an asymmetric Smoluchowski equation.Comment: 5 pages, 5 figure
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